CN109670625B - NOx emission concentration prediction method based on unscented Kalman filtering least square support vector machine - Google Patents

NOx emission concentration prediction method based on unscented Kalman filtering least square support vector machine Download PDF

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CN109670625B
CN109670625B CN201810992640.3A CN201810992640A CN109670625B CN 109670625 B CN109670625 B CN 109670625B CN 201810992640 A CN201810992640 A CN 201810992640A CN 109670625 B CN109670625 B CN 109670625B
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张友卫
曹硕硕
周春蕾
曾令超
帅云峰
孙栓柱
李益国
王林
李春岩
杨晨琛
李逗
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State Grid Corp of China SGCC
Southeast University
State Grid Jiangsu Electric Power Co Ltd
Jiangsu Fangtian Power Technology Co Ltd
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Southeast University
State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a coal-fired unit NOx emission concentration prediction method based on an unscented Kalman filtering least square support vector machine. Determining input and output variables of a dynamic model of the denitration system through analysis of field data and theory, finishing prediction of NOx emission concentration at the current moment through offline calculation of parameters of the dynamic model of the denitration system, continuously updating a kernel parameter value sigma and model parameters alpha and b by adopting unscented Kalman filtering, updating a support vector sample, and predicting the NOx emission concentration at the next moment. The method provided by the invention can accurately predict the NOx emission concentration, is beneficial to further improving the regulation quality of the selective catalytic reduction denitration control system, can be used for judging whether field data is real and accurate, and provides a basis for supervision and law enforcement of environmental protection departments.

Description

NOx emission concentration prediction method based on unscented Kalman filtering least square support vector machine
Technical Field
The invention belongs to the technical field of thermal power environmental protection monitoring, and particularly relates to a NOx (nitrogen oxide) emission concentration prediction method based on an Unscented Kalman Filter Least square Support Vector Machine (UKF-LSSVM).
Background
With the strong promotion of energy-saving and emission-reducing policies, the emission of nitrogen oxides is more and more valued by environmental protection departments. A coal-fired boiler of a power plant is one of important sources of nitrogen oxides in the environment, and a Selective Catalytic Reduction (SCR) denitration technology is widely used in a thermal power plant at present. However, the denitration system is complex in interior, and coupling correlation among parameter variables is serious, so that the establishment of a corresponding physical model is very difficult. With the wide application of the distributed control system, a large number of operation parameters of the unit and auxiliary equipment related to the operation state are recorded, and with the development of various artificial intelligence and advanced algorithms and the successful application in industry, the research on system data modeling of the denitration system is developed.
The work of predicting and modeling the emission concentration of NOx emitted by a coal-fired unit is relatively less, the emission concentration of NOx emitted by the coal-fired unit is accurately predicted by using relevant operation parameters of the unit, whether field acquisition data is real and accurate can be judged, a basis is provided for supervision and law enforcement of environmental protection departments, and meanwhile, the regulation quality of an SCR control system can be greatly improved and ammonia escape is reduced by combining advanced control strategies such as prediction control, so that the method has important theoretical significance and practical value. Compared with an off-line least square support vector machine algorithm, the model can be updated in time according to the change of the object characteristics, and the method has adaptivity, but the parameter sigma needs to be set in advance, and the prediction performance of the least square support vector machine is greatly influenced.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for predicting NOx emission concentration based on an unscented Kalman filter least square support vector machine aiming at the defects of the prior art.
In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:
the method for predicting the NOx emission concentration based on the unscented Kalman filtering least square support vector machine comprises the following steps:
s1: selecting the concentration of NOx discharged by a coal-fired unit as prediction output, and determining a state parameter related to the concentration as an input variable of a model;
s2: sampling at the same frequency, and respectively removing gross errors and normalizing the original data by adopting an improved observed quantity change rate method and an upper and lower limit normalization method;
s3: selecting initial sample data according to the input and output structure of the dynamic model, calculating initial parameters alpha, b and sigma of the dynamic model of the denitration system in an off-line manner based on a least square support vector machine method, and obtaining a model prediction function at the same time;
s4: according to the model prediction function, the model prediction value of the current moment is input and calculated from the previous moment, and the model prediction error is calculated;
s5: judging whether the error exceeds the allowed maximum error, if not, the dynamic model is not corrected, the model parameters are not changed, and returning to the step S4 to continuously calculate the predicted value of the model at the next moment; if the error threshold value is exceeded, updating the model parameters sigma, alpha and b through the unscented transformation, updating the training sample data at the same time, and returning to the step S4 to continuously calculate the predicted value of the model at the next moment.
In the above step S1, the pearson correlation coefficient r is used to measure the correlation of the variables:
Figure GDA0003628713110000021
in the formula, xiIth sample value, y, for NOx concentration emitted by coal-fired unitiThe i-th sampled value of the state parameter related to the NOx concentration, N is the total number of samples,
Figure GDA0003628713110000022
are the average values of the two sets of variables, respectively; the larger the value of r, the larger the correlation between the two variables, and a correlation threshold r is set0Selecting r value exceeding r0As input variables.
The above-described removal and normalization processing of the gross error in step S2 includes the steps of:
s2.1: the method for detecting the change rate of the improved observed quantity is adopted, whether the change quantity of the observed quantity at the current moment and the previous moment exceeds 3 times of standard deviation is judged to eliminate a coarse error, the change quantity between two adjacent moments is taken as an object, the 3 times of standard deviation criterion is improved, so that the threshold has self-adaptability, and the calculation formula is as follows:
Δxj＝x(n-Nh+j)-x(n-Nh+j-1) (2)
wherein j is 2,3, … Nh；
Figure GDA0003628713110000023
Figure GDA0003628713110000031
Whereby an improved rate of change of the observed quantity is obtained
Figure GDA0003628713110000032
And judging a gross error by using a 3-time standard deviation criterion;
s2.2: and (3) adopting an upper and lower limit normalization method to normalize all sample data to be between [0 and 1], wherein the formula is as follows:
Figure GDA0003628713110000033
wherein x and x' are sample values before and after normalization, respectivelymin、xmaxMinimum and maximum values in the sample data.
In the step S3, the off-line calculation of the initial parameters of the dynamic model of the denitration system based on the least square support vector machine method and the obtaining of the model prediction function include the following steps:
for the training sample set T { (x)1,y1),…,(xN,yN) In which xi∈Rd，yiE, R, i is 1,2, …, N, N is the number of training samples, and an optimal decision function is constructed in a high-dimensional feature space
Figure GDA0003628713110000034
The problem is converted into solving the minimized structure risk, and the formula is as follows:
Figure GDA0003628713110000035
Figure GDA0003628713110000036
wherein w and b are model parameters, c is a penalty factor,
Figure GDA0003628713110000037
as a non-line from the input space to the high-dimensional feature spaceSexual mapping, eiIs a prediction error;
the Lagrange function corresponding to this is:
Figure GDA0003628713110000038
wherein α ═ α1 α2 … αN]For Lagrange multipliers, according to the optimized Karush-Kuhn-Tucker (KKT) condition:
Figure GDA0003628713110000039
and (3) combining Lagrange function expression (8) and KKT optimization condition expression (9) to obtain a linear equation system of the optimization problem:
Figure GDA0003628713110000041
in the formula (I), the compound is shown in the specification,
Figure GDA0003628713110000042
Figure GDA0003628713110000043
y＝[y1 y2 … yN]T (13)
Figure GDA0003628713110000044
in the formula (I), the compound is shown in the specification,
Figure GDA0003628713110000045
taking the radial basis function as a kernel function:
Figure GDA0003628713110000046
and (3) combining the formula (10) with the formula (14) to obtain an optimal decision function, and obtaining a predicted value at the current moment by inputting the predicted value at the previous moment, wherein the optimal decision function, namely a model prediction function, is as follows:
Figure GDA0003628713110000047
the above step S5 specifically includes the following steps:
for a random variable x ∈ RdThe expected value and covariance matrix are respectively
Figure GDA0003628713110000048
P0Wherein
Figure GDA0003628713110000049
P0Initially, a unit matrix is set, and a nonlinear transformation is performed by y ═ g (x) e RmY is a matrix x consisting of a pointk-1∈R2d+1The result is that the number of the first and second,
Figure GDA00036287131100000410
Figure GDA00036287131100000411
Figure GDA00036287131100000412
Figure GDA00036287131100000413
wherein psi ═ gamma2(d + k) -d is a screening parameter, gamma determines the dispersion degree of sigma points, the parameter k is 0, theta represents the distribution information of sampling points and is 2, and chiz,k-1Is xk-1Is in the z-th column of (1),
Figure GDA0003628713110000051
is the z-th column of the square root of the matrix, WmkIs the desired weight, Wc, of the kth sample pointkThe weight of the k sampling point variance is obtained;
the method for estimating the parameters by using the unscented Kalman filtering comprises the following steps:
s5.1 initialization:
Figure GDA0003628713110000052
Figure GDA0003628713110000053
s5.2 σ Point Generation:
Figure GDA0003628713110000054
s5.3 time update:
χz,k|k-1＝F(χz,k-1) (23)
Figure GDA0003628713110000055
Figure GDA0003628713110000056
yz,k|k-1＝G(χz,k|k-1) (26)
Figure GDA0003628713110000057
s5.4 parameter updating:
Figure GDA0003628713110000058
Figure GDA0003628713110000059
Figure GDA00036287131100000510
Figure GDA00036287131100000511
Figure GDA00036287131100000512
obtaining next moment by iterative solution
Figure GDA00036287131100000513
And PkValue of, from
Figure GDA00036287131100000514
Obtaining the model parameter values b, alpha and sigma at the next moment;
s5.5, updating a sample:
when the prediction error is larger, the sample needs to be updated online, the corresponding sample with the minimum alpha value is replaced by the current sample, and the current sample is set as { x+,y+In which x is+＝[x1,x2,…xN]T，y+＝[y1,y2…yN]TIt has been determined to remove { x from the set of support vectorsj,yjAnd f, the new training samples are:
xnew+＝[x1,…xj-1,xN,xj+1…xN-1]T，ynew+＝[y1,…yj-1,yN,yj+1…yN-1]T。
the invention has the following beneficial effects:
the unscented Kalman filter is used for updating the kernel parameter sigma value, so that the adaptivity of the online least square support vector machine is further improved, the prediction precision and the generalization capability are better, and an ideal effect can be achieved when fewer training samples are available.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a sample set of initial training samples of a prediction model according to an embodiment of the present invention;
FIG. 3 is a Pearson correlation coefficient plot of NOx emission concentration for a coal fired unit in an embodiment of the present invention;
FIG. 4 is a diagram of a model for predicting NOx concentration emitted from a coal-fired unit according to an embodiment of the present invention;
FIG. 5 is a diagram showing the prediction results of the LSSVM model in embodiment 1 of the present invention;
FIG. 6 is a diagram of the predicted result of the UKF-LSSVM model in embodiment 1 of the present invention;
FIG. 7 is a diagram of the prediction result of the UKF-LSSVM model in embodiment 2 of the present invention;
FIG. 8 is a graph of variation of the kernel parameter σ with load in the UKF-LSSVM model in embodiment 2 of the present invention.
Detailed Description
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
Example 1: the method for predicting the NOx emission concentration based on the unscented Kalman filtering least square support vector machine comprises the following specific steps as shown in figure 1:
step 1: a certain 300MW coal-fired power plant boiler is taken as a research object, and an SCR denitration system device which is relatively mature in technology and relatively wide in application is adopted. The selected data time span is one month, the sampling time is 5s, and the data comprises steady-state data in a normal and stable running state of the system and unsteady-state data in variable load. And selecting 5000 sample points under the condition of load change for modeling simulation. Through repeated experiments, under the condition of considering both the operation speed and the model precision, the number of training samples is selected to be 10, the first 10 samples of the initial sample set are taken as training samples, and the prediction model initial training sample set is shown in fig. 2.
Wherein: pe(t-1) is the unit load; xin1(t-1)、Xin2(t-1) NOx concentration at inlets of the SCR reactors at two sides; xN1(t-1)、XN2(t-1) the amount of ammonia sprayed on both sides; xou1(t-1)、Xou2(t-1) NOx concentration at inlets of the SCR reactors at two sides; y isNOx(t-2)、YNOx(t-1)、YNOxAnd (t) is the concentration of NOx discharged by the coal-fired unit at different sampling moments.
The degree of closeness of the relationship between the variables is checked according to the Pearson correlation coefficient, and the formula is as follows:
Figure GDA0003628713110000071
in the formula, xiIth sample value, y, for NOx concentration emitted by coal-fired unitiThe i-th sampled value of the state parameter associated with the NOx concentration, N is the total number of samples,
Figure GDA0003628713110000072
are the average values of the two sets of variables, respectively;
pearson correlation coefficients between the candidate variables and the NOx emission concentration of the coal-fired unit are respectively calculated, and specific data are shown in a graph 3. And selecting a variable with the Pearson correlation coefficient | r | ≧ 0.15 as an auxiliary variable of the NOx emission concentration prediction model. And finally, selecting the concentration of NOx at the outlets of the SCR reactors at two sides, the ammonia injection amount of the mixers at two sides, the concentration of NOx at the inlets of the reactors at two sides and the load of the unit as input variables of a prediction model, and taking the concentration of NOx discharged by the coal-fired unit as output variables of the model. The difference from the steady-state modeling is that the dynamic modeling adds the order of the variables to the input and output, and the structure of the specific denitration system dynamic model is shown in fig. 4.
Step 2: the sampling frequency of all data is the same, the coarse error of the original data is removed by adopting an improved observation quantity change rate method, and the data is normalized;
s2.1: and (3) eliminating a coarse error by adopting an improved observation quantity change rate detection method and judging whether the observation quantity change quantity of the current moment and the previous moment exceeds 3 times of a standard deviation (3 sigma). Aiming at the variation between two adjacent moments, the 3 sigma criterion is improved to make the threshold adaptive, and the calculation formula is as follows:
Δxi＝x(n-Nh+i)-x(n-Nh+i-1) (2)
wherein i is 2,3, … Nh；
Figure GDA0003628713110000073
Figure GDA0003628713110000074
Whereby an improved observation rate of change is determined
Figure GDA0003628713110000075
And used for the 3 sigma criterion for gross error determination.
S2.2: and (3) adopting an upper and lower limit normalization method to normalize all sample data to be between [0,1 ]. The formula is as follows:
Figure GDA0003628713110000081
wherein x and x' are sample values before and after normalization, respectivelymin、xmaxMinimum and maximum values in the sample data.
S3: selecting initial sample data according to the input and output structure of the dynamic model, and calculating the initial parameters of the dynamic model of the denitration system in an off-line manner based on a least square support vector machine method;
and step 3: according to an input and output structure of a dynamic model, selecting the first 10 sample sets as initial sample data, calculating initial parameters of the dynamic model of the denitration system in an off-line mode based on a least square support vector machine method, wherein the initial parameters are respectively alpha [ -2.55-2.171.351.421.22-1.002.94-2.22-1.192.21 ] and b ═ 0.411, and the sigma initial value is set to be 3;
and 4, step 4: inputting and calculating a model prediction value of the current moment from the previous moment, and calculating a model prediction error;
and 5: judging whether the error exceeds the allowed maximum error, if not, the dynamic model does not need to be corrected, the model parameters are kept unchanged, and returning to the step S4 to continuously calculate the predicted value of the model at the next moment; and if the error threshold is exceeded, updating the model parameters sigma, alpha and b through unscented Kalman, updating the training sample data, returning to the step S4 to continuously calculate the model predicted value at the next moment until the concentration of NOx discharged by the coal-fired unit at 5000 moments is completely predicted.
The model accuracy evaluation standard selects a root mean square error and an average absolute percentage error to evaluate the accuracy degree of the UKF-LSSVM and LSSVM models, and the calculation formula is as follows:
Figure GDA0003628713110000082
Figure GDA0003628713110000083
in the formula, yiIs a measure of the amount of time that,
Figure GDA0003628713110000084
is a predicted value.
As shown in fig. 6, it can be seen from a comparison between fig. 5 and 6 that MAPE and RMSE of the UKF-LSSVM method are 0.17% and 0.0707mg/m, respectively-3The prediction model has high precision, and the two groups of indexes are respectively smaller than the indexes of the LSSVM, MAPE is 3.83%, and RMSE is 2.4166mg/m-3The UKF-LSSVM can more accurately predict the concentration value of the NOx discharged by the coal-fired unit compared with the LSSVM, has better prediction precision and stronger self-adaptive capacity,
example 2: the present example is different from example 1 in that the initial value of σ is set to 0.1, and other steps and parameters are the same as those of example 1. When the initial value of sigma is set to 0.1, the prediction result of the UKF-LSSVM model is shown in FIG. 7, the variation of the kernel parameter sigma in the UKF-LSSVM model along with the load is shown in FIG. 8, and as can be seen from FIG. 7 and FIG. 8, the UKF-LSSVM model still obtains a good prediction result for any given initial value of the kernel parameter, the model precision is not influenced by the initial kernel parameter sigma value, so that the difficulty in selecting sigma is greatly reduced, and the method has an important effect on facilitating the practical application of the method.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (4)

1. The prediction method of the NOx emission concentration based on the unscented Kalman filtering least square support vector machine is characterized by comprising the following steps: the method comprises the following steps:
step S1: selecting the concentration of NOx discharged by a coal-fired unit as prediction output, and determining a state parameter related to the concentration as an input variable of a model;
step S2: sampling at the same frequency, and respectively removing gross errors and normalizing the original data by adopting an improved observed quantity change rate method and an upper and lower limit normalization method;
step S3: selecting initial sample data according to the input and output structure of the dynamic model, calculating initial parameters alpha, b and sigma of the dynamic model of the denitration system in an off-line manner based on a least square support vector machine method, and obtaining a model prediction function at the same time;
step S4: according to the model prediction function, the model prediction value of the current moment is input and calculated from the previous moment, and the model prediction error is calculated;
step S5: judging whether the error exceeds the allowed maximum error, if not, the dynamic model is not corrected, the model parameters are not changed, and returning to the step S4 to continuously calculate the predicted value of the model at the next moment; if the error threshold is exceeded, updating the model parameters sigma, alpha and b through unscented transformation, updating training sample data at the same time, and returning to the step S4 to continuously calculate the model predicted value at the next moment;
the step S3 of calculating the initial parameters of the dynamic model of the denitration system in an off-line manner based on the least square support vector machine method and obtaining the model prediction function at the same time comprises the following steps:
for the training sample set T { (x)1,y1),…,(xN,yN) In which x isi∈Rd，yiE, R, i is 1,2, …, N, N is the number of training samples, and an optimal decision function is constructed in a high-dimensional feature space
Figure FDA0003579445220000011
The problem is converted into solving the minimized structure risk, and the formula is as follows:
Figure FDA0003579445220000012
Figure FDA0003579445220000013
wherein w and b are model parameters, c is a penalty factor,
Figure FDA0003579445220000014
for non-linear mapping from the input space to the high-dimensional feature space, eiIs a prediction error;
the Lagrange function corresponding to this is:
Figure FDA0003579445220000015
wherein α ═ α1 α2…αN]For Lagrange multipliers, according to the optimized Karush-Kuhn-Tucker (KKT) condition:
Figure FDA0003579445220000021
and (3) combining Lagrange function expression (8) and KKT optimization condition expression (9) to obtain a linear equation system of the optimization problem:
Figure FDA0003579445220000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003579445220000023
Figure FDA0003579445220000024
y＝[y1 y2…yN]T (13)
Figure FDA0003579445220000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003579445220000026
taking the radial basis function as a kernel function:
Figure FDA0003579445220000027
combining the formula (10) and the formula (14) to obtain an optimal decision function, and obtaining a predicted value of the current time from the input of the previous time, wherein the optimal decision function, namely a model prediction function, is as follows:
Figure FDA0003579445220000028
2. the unscented kalman filter least squares support vector machine-based NOx emission concentration prediction method according to claim 1, characterized by: in step S1, the pearson correlation coefficient r is used to measure the correlation of the variables:
Figure FDA0003579445220000029
in the formula, xiIth sample value, y, for NOx concentration emitted by coal-fired unitiThe i-th sampled value of the state parameter related to the NOx concentration, N is the total number of samples,
Figure FDA00035794452200000210
are the average values of the two sets of variables, respectively; the larger the value of r, the larger the correlation between the two variables, and a correlation threshold r is set0Selecting r value exceeding r0As input variables.
3. The method of claim 1 for predicting NOx emission concentration based on unscented Kalman filter least squares support vector machines, characterized by: the coarse error removal and normalization process of step S2 includes the following steps:
s2.1: the method for detecting the change rate of the improved observed quantity is adopted, whether the change quantity of the observed quantity at the current moment and the previous moment exceeds 3 times of standard deviation is judged to eliminate a coarse error, the change quantity between two adjacent moments is taken as an object, the 3 times of standard deviation criterion is improved, so that the threshold has self-adaptability, and the calculation formula is as follows:
Δxj＝x(n-Nh+j)-x(n-Nh+j-1) (2)
wherein j is 2,3, … Nh；
Figure FDA0003579445220000031
Figure FDA0003579445220000032
Whereby an improved observation rate of change is determined
Figure FDA0003579445220000033
And judging a gross error by using a 3-time standard deviation criterion;
s2.2: and (3) adopting an upper and lower limit normalization method to normalize all sample data to be between [0 and 1], wherein the formula is as follows:
Figure FDA0003579445220000034
wherein x and x' are respectively the sample values before and after normalization, xmin、xmaxMinimum and maximum values in the sample data.
4. The method of predicting NOx emission concentration based on unscented Kalman filter least squares support vector machine according to claim 1, characterized in that: the specific steps of the traceless transformation in step S5 are:
for a random variable x ∈ RdThe expected value and covariance matrix are respectively
Figure FDA0003579445220000035
P0Wherein
Figure FDA0003579445220000036
P0Initially, a unit matrix is set, and a nonlinear transformation is performed by y ═ g (x) e RmY is a matrix x consisting of a pointk-1∈R2d+1The result is that,
Figure FDA0003579445220000037
Figure FDA0003579445220000038
Figure FDA0003579445220000039
Figure FDA00035794452200000310
wherein psi ═ gamma2(d + k) -d is a screening parameter, gamma determines the dispersion degree of sigma points, the parameter k is 0, theta represents the distribution information of sampling points and is 2, and chiz,k-1Is xk-1Is in the z-th column of (1),
Figure FDA0003579445220000041
is the z-th column of the square root of the matrix, WmkIs the desired weight, Wc, of the kth sample pointkThe weight of the k sampling point variance is obtained;
the method for estimating the parameters by using the unscented Kalman filtering comprises the following steps:
s5.1 initialization:
Figure FDA0003579445220000042
Figure FDA0003579445220000043
s5.2. Generation of σ Point:
Figure FDA0003579445220000044
s5.3 time update:
χz,k|k-1＝F(χz,k-1) (23)
Figure FDA0003579445220000045
Figure FDA0003579445220000046
yz,k|k-1＝G(χz,k|k-1) (26)
Figure FDA0003579445220000047
s5.4 parameter updating:
Figure FDA0003579445220000048
Figure FDA0003579445220000049
Figure FDA00035794452200000410
Figure FDA00035794452200000411
Figure FDA00035794452200000412
obtaining next moment by iterative solution
Figure FDA00035794452200000413
And PkValue of, from
Figure FDA00035794452200000414
Obtaining the model parameter values b, alpha and sigma at the next moment;
s5.5, updating a sample:
when the prediction error is larger, the sample needs to be updated on line, the corresponding sample with the minimum alpha value is replaced by the current sample, and the current sample is set as { x+,y+In which x+＝[x1,x2,…xN]T，y+＝[y1,y2…yN]TIt has been determined to remove { x from the set of support vectorsj,yjAnd f, the new training samples are:
xnew+＝[x1,…xj-1,xN,xj+1…xN-1]T，ynew+＝[y1,…yj-1,yN,yj+1…yN-1]T。
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* Cited by examiner, † Cited by third party
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CN104091216A (en) * 2014-07-29 2014-10-08 吉林大学 Traffic information predication method based on fruit fly optimization least-squares support vector machine
CN106096646A (en) * 2016-06-07 2016-11-09 衢州学院 A kind of support vector regression model selection method
CN106680428A (en) * 2016-12-19 2017-05-17 华北电力大学（保定） Soft measuring method for denitration control system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104091216A (en) * 2014-07-29 2014-10-08 吉林大学 Traffic information predication method based on fruit fly optimization least-squares support vector machine
CN106096646A (en) * 2016-06-07 2016-11-09 衢州学院 A kind of support vector regression model selection method
CN106680428A (en) * 2016-12-19 2017-05-17 华北电力大学（保定） Soft measuring method for denitration control system

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